Sample paper · GCSE Foundation · grades 1–5
GCSE Foundation sample Paper 1 (non-calculator)
The real Paper 1 is 1.5 hour 30 minutes and 80 marks, non-calculator, and all three papers carry equal weight. This sample is 20 original questions in the same content proportions as the Foundation qualification — number 25%, algebra 20%, ratio, proportion and rates of change 25%, geometry and measures 15%, probability 7.5%, statistics 7.5% — with no calculator-only items. AO1 / AO2 / AO3 at this tier: 50% / 25% / 25%.
Non-calculatorGCSE Foundation
GCSE Foundation sample Paper 1 (non-calculator)
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- 1.Work out ⁴√81
- 2.Which of these equations gives a graph shaped like a U, symmetrical about a vertical line?
- 3.8 identical pens cost £6.40 in total. Work out the cost of 5 of the same pens.
- 4.Work out the exact value of tan 30° + tan 30°.
- 5.A two-way table records how 80 students travel to school. 45 of the students are boys and the rest are girls. 27 of the boys walk to school. Work out the probability, as a fraction, that a student chosen at random from the boys walks to school.
- 6.In a vertical line chart of test results, the tallest line stands for 40 pupils. The same results are to be shown in a pie chart of all 100 pupils. Work out the angle at the centre of the sector that will stand for those 40 pupils.
- 7.A shortbread recipe uses flour and butter in the ratio 5 : 2. Yuki changes the recipe by doubling the amount of butter but keeping the amount of flour the same. Work out the fraction of the new mixture that is butter.
- 8.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.
- 9.Two mathematically similar flags are made in different sizes. The length scale factor from the smaller flag to the larger flag is 5. Work out the area scale factor from the smaller flag to the larger flag.
- 10.A right-angled triangle has a hypotenuse of 14 cm. One of the other angles is 30°. Work out the exact length of the side opposite the 30° angle.
- 11.Two events are independent. The first has probability 2/5 and the second has probability 1/3. Work out the probability that both events happen.
- 12.A space probe is 7.5 × 10⁸ km from Earth. Write this distance as an ordinary number.
- 13.The diagram shows the graph of a quadratic function. Write down the values of x where the graph crosses the x-axis.
- 14.Three numbers are in the ratio 1:2:3. The three numbers add up to 72. Work out the largest of the three numbers.
- 15.A line segment is measured with a ruler and found to be 6.5 cm long. What is this length in millimetres?
- 16.Grace works out 7 × 99 by writing 99 as 100 − 1. Use her method to work out 7 × 99.
- 17.A company's profit is £500 in its first year. Each year after that, the profit is £300 more than the year before. Work out the profit in the company's 6th year.
- 18.Write 45 minutes : 2 hours as a ratio in its simplest form.
- 19.Work out (4 × 10⁻³) × (2 × 10⁵). Give your answer in standard form.
- 20.A recipe uses flour, sugar and butter in the ratio 8 : 3 : 5. Write the ratio of flour to the rest of the mixture (sugar and butter combined) in its simplest form.
How the 20 questions are shared out
- Number — 5 questions (25% of the qualification)
- Algebra — 4 questions (20% of the qualification)
- Ratio, proportion and rates of change — 5 questions (25% of the qualification)
- Geometry and measures — 3 questions (15% of the qualification)
- Probability — 2 questions (7.5% of the qualification)
- Statistics — 1 question (7.5% of the qualification)
Where an area has fewer printable questions than its share, the shortfall is filled from the other areas. These are original questions, not past papers.